Johansen cointegration test
[h,pValue,stat,cValue,mles]
= jcitest(Y)
[h,pValue,stat,cValue,mles]
= jcitest(Y,Name,Value)
Johansen tests assess the null hypothesis H(r) of
cointegration rank less than or equal to r among
the numDims
dimensional time series in Y
against
alternatives H(numDims
) (trace
test)
or H(r+1) (maxeig
test).
The tests also produce maximum likelihood estimates of the parameters
in a vector errorcorrection (VEC) model of the cointegrated series.
[
performs the Johansen
cointegration test on a data matrix h
,pValue
,stat
,cValue
,mles
]
= jcitest(Y
)Y
.
[
performs
the Johansen cointegration test on a data matrix h
,pValue
,stat
,cValue
,mles
]
= jcitest(Y
,Name,Value
)Y
with
additional options specified by one or more Name,Value
pair
arguments.


Specify optional commaseparated pairs of Name,Value
arguments.
Name
is the argument
name and Value
is the corresponding
value. Name
must appear
inside single quotes (' '
).
You can specify several name and value pair
arguments in any order as Name1,Value1,...,NameN,ValueN
.

Character vector, such as $$\Delta {y}_{t}=C{y}_{t1}+{B}_{1}\Delta {y}_{t1}+\dots +{B}_{q}\Delta {y}_{tq}+DX+{\epsilon}_{t}$$ If r < Values of
Deterministic terms outside of the cointegrating relations, c_{1} and d_{1}, are identified by projecting constant and linear regression coefficients, respectively, onto the orthogonal complement of A.  

Scalar or vector of nonnegative integers indicating the number q of lagged differences in the VEC(q) model of y_{t}. Lagging and differencing a time series reduce the sample size. Absent any presample values, if y_{t} is defined for t = 1:N, then the lagged series y_{t−k} is defined for t = k + 1:N. Differencing reduces the time base to k+2:N. With q lagged differences, the common time base is q+2:N and the effective sample size is T = N−(q+1). Default: 0  

Character vector, such as
 

Scalar or vector of nominal significance levels for the tests. Values must be between 0.001 and 0.999. Default: 0.05  

Character vector, such as
Character vectors values are expanded to the length of any vector value (the number of tests). Vector values must have equal length. 

Rows of Values of  

Rows of  

Rows of  

Rows of  

Rows of 
Time series in Y
might be stationary in
levels or first differences (i.e., I(0) or I(1)).
Rather than pretesting series for unit roots (using, e.g., adftest
, pptest
, kpsstest
, or lmctest
),
the Johansen procedure formulates the question within the model. An I(0)
series is associated with a standard unit vector in the space of cointegrating
relations, and its presence can be tested using jcontest
.
If jcitest
fails to reject the null of
cointegration rank r = 0,
the inference is that the errorcorrection coefficient C is
zero, and the VEC(q) model reduces to a standard
VAR(q) model in first differences. If jcitest
rejects
all cointegration ranks r less than numDims
,
the inference is that C has full rank, and y_{t} is
stationary in levels.
The parameters A and B in
the reducedrank VEC(q) model are not uniquely
identified, though their product C = AB′ is. jcitest
constructs B
= V
(:,1:r)
using the orthonormal eigenvectors V
returned by eig
, then renormalizes so that V'*S11*V
= I
, as in [2].
To test linear constraints on the errorcorrection speeds A and
the space of cointegrating relations spanned by B,
use jcontest
.
To convert VEC(q) model parameters in the mles
output
to VAR(q+1)
model parameters, use vec2var
.
[1] Hamilton, J. D. Time Series Analysis. Princeton, NJ: Princeton University Press, 1994.
[2] Johansen, S. LikelihoodBased Inference in Cointegrated Vector Autoregressive Models. Oxford: Oxford University Press, 1995.
[3] MacKinnon, J. G., A. A. Haug, and L. Michelis. "Numerical Distribution Functions of Likelihood Ratio Tests for Cointegration." Journal of Applied Econometrics. v. 14, 1999, pp. 563–577.
[4] Turner, P. M. "Testing for Cointegration Using the Johansen Approach: Are We Using the Correct Critical Values?" Journal of Applied Econometrics. v. 24, 2009, pp. 825–831.